Implicit Linear Systems

This set of notes is an introduction to implicit models of linear dynamic systems, with applications for modelling, control system design and identification, intended for control-system engineers at new graduate level. The models given are non-oriented and are therefore useful in cases where causality is unknown or may change. The notes simplify and complement recent work on "singular" or "descriptor" models. Sections are included on realizations, canonical forms, minimal representations, algebraic design applications, quadratic optimization, identification, large-scale systems and extensions to multi-dimensional and time-varying systems.